# Does the equation 7x - 4y = 0 represent a direct variation? If so, find the constant of...

## Question:

Does the equation 7x - 4y = 0 represent a direct variation? If so, find the constant of variation.

A) yes; {eq}k= \frac{7}{4} {/eq}

B) yes, k= -4

C) No

D) yes; {eq}k= \frac{-7}{4} {/eq}

## Direct and Inverse Variation:

Direct Variation:

• If x varies directly as y then {eq}x=ky {/eq}, where 'k' is a constant of variation.

Inverse Variation:

• If x varies inversely as y then {eq}x= \dfrac{m}{y} {/eq}, where 'm' is a constant of variation.

The given equation is:

$$7x - 4y = 0 \\ \text{Subtracting 7x from both sides}: \\ -4y=-7x \\ \text{Dividing both sides by -4}, \\ y= \dfrac{7}{4}x$$

This is of the form {eq}y=kx {/eq}. So this represents a direct variation.

The constant of variation is, {eq}k= \boxed{\mathbf{ \dfrac{7}{4}}} {/eq}.